Fixed point results and the Ekeland variational principle in vector $B$-metric spaces
Functional Analysis
2025-02-17 v1
Abstract
In this paper, we extend the concept of -metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the -metric setting: fixed-point theorems, stability results, and a variant of Ekeland's variational principle. As a consequence, we also derive a variant of Caristi's fixed-point theorem
Keywords
Cite
@article{arxiv.2502.09634,
title = {Fixed point results and the Ekeland variational principle in vector $B$-metric spaces},
author = {Radu Precup and Andrei Stan},
journal= {arXiv preprint arXiv:2502.09634},
year = {2025}
}